If the equation `2x^2+4x y+7y^2-12 x-2y+t=0,w h e r et` is a parameter has exactly one real solution of hte form `(x ,y)` , then hte sum of `(x+y)` is equal to ______.

If y=y(x) and it follows the relation 4x e^(x y)=y+5sin^2x , then y^(prime)(0) is equal to______

If f(2x+3y, 2x-7y)=20x, then f(x,y) equals :

3x-4y=-7,5x-2y=0

The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by

Consider the equation 2/x+5/y=1/3w h e r ex ,y in Ndot Find the number of solutions of the equation.

If (log)_(10)(x^3+y^3)-(log)_(10)(x^2+y^2-x y)lt=2,w h e r ex ,y are positive real number, then find the maximum value of x ydot

If the pairs of lines x^2+2x y+a y^2=0 and a x^2+2x y+y^2=0 have exactly one line in common, then the joint equation of the other two lines is given by (a) 3x^2+8x y-3y^2=0 (b) 3x^2+10 x y+3y^2=0 (c) y^2+2x y-3x^2=0 (d) x^2+2x y-3y^2=0

The system of equations x +2y+3z=1, x-y+4z=0, 2x+y+7z=1 has

Let y = y(x) be the solution of the differential equation x dy/dx+y=xlog_ex,(xgt1)." If " 2y(2)=log_e4-1," then "y(e) is equal to